含裂纹平面问题Erdogan基本解的显式表达

许秩; 范学明

doi:10.21656/1000-0887.370253

含裂纹平面问题Erdogan基本解的显式表达

doi: 10.21656/1000-0887.370253

许秩¹,
范学明^1,2

¹华南理工大学土木与交通学院, 广州 510640;²亚热带建筑科学国家重点实验室(华南理工大学), 广州 510640

基金项目: 国家自然科学基金(面上项目)(51378009)；高等学校博士学科点专项科研基金新教师类课题(20110172120038)；中央高校基本科研业务费(2015ZM116)；国家级大学生创新创业训练计划项目(201610561171)

详细信息

作者简介:
许秩（1992—），男，博士生(E-mail: stxuz@163.com);范学明（1979—），男，讲师，博士(通讯作者. E-mail: fanxm@scut.edu.cn).

中图分类号: O343.1
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- 文章访问数: 980
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- 被引次数: 0
出版历程
- 收稿日期: 2016-08-16
- 修回日期: 2017-05-11
- 刊出日期: 2017-09-15

The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

XU Zhi¹,
FAN Xue-ming^1,2

¹School of Civil Engineering and Transportation, South China University of Technology, Guangzhou 510640, P.R.China;²State Key Laboratory of Subtropical Building Science(South China University of Technology), Guangzhou 510640, P.R.China

Funds: The National Natural Science Foundation of China(General Program)(51378009)

摘要

摘要: 基本解是边界元法、基本解法和无网格法等数值方法的重要理论基础.在断裂问题中,采用含裂纹的基本解可以避免将裂纹表面作为边界条件，从而大大简化问题的求解.在复变函数表示的含裂纹平面问题Erdogan基本解的基础上，对Erdogan基本解的使用条件进行了注解，修正了Erdogan基本解的一些错误，并推导出Erdogan基本解中位移函数解答的显式表达形式.编写了基于Erdogan基本解显式表达的样条虚边界元法（spline fictitious boundary element method, SFBEM）计算程序，计算了具有复合边界条件平面问题的位移、应力和应力强度因子.数值算例结果表明了该文提出的Erdogan基本解显式表达形式的正确性.
- 断裂力学 /
- Erdogan基本解 /
- 显式表达 /
- 样条虚边界元法
Abstract: The fundamental solution plays an essential role in many numerical methods such as the boundary element method (BEM), the method of fundamental solution and the boundarytype meshless methods. For fracture problems, application of fundamental solutions in domains with cracks can avoid deeming the crack surface as boundary condition and simplify the problems significantly. Based on the complex variable expression of Erdogan’s fundamental solution (EFS) for plane problems, the application conditions for EFS were noted, some faults in EFS were corrected and the explicit expression of the displacement in EFS was obtained. The computer program of the spline fictitious boundary element method (SFBEM) based on EFS was compiled to calculate the numerical solutions to mixed boundary condition problems. Numerical examples prove the correctness and accuracy of the derived explicit expression of EFS.
- fracture mechanics /
- Erdogan’s fundamental solution /
- explicit expression /
- spline fictitious boundary element method

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参考文献(17)

[1]	郦正能. 应用断裂力学[M]. 北京: 北京航空航天大学出版社, 2012.(LI Zheng-neng. Applied Fracture Mechanics [M]. Beijing: Beihang University Press, 2012.(in Chinese))
[2]	Zehnder A T. Fracture Mechanics [M]. Netherlands: Springer, 2012.
[3]	付宇明, 田振国, 郑丽娟. 轴对称金属模具电磁热裂纹止裂中热应力场的分析[J]. 应用数学和力学, 2006,27(3): 331-336.(FU Yu-ming, TIAN Zhen-guo, ZHENG Li-juan. Thermal stress field when crack arrest in an axial symmetry metal die using electromagnetic heating[J]. Applied Mathematics and Mechanics,2006,27(3): 331-336.(in Chinese))
[4]	Benzley S E. Representation of singularities with isoparametric finite elements[J]. Clinical Endocrinology,1974,8(8): 537-545.
[5]	Tan M A, Meguid S A. Analysis of bimaterial wedges using a new singular finite element[J]. International Journal of Fracture,1997,88(4): 373-391.
[6]	MENG Qing-hua, WANG Zhen-qing. Extended finite element method for power-law creep crack growth[J]. Engineering Fracture Mechanics,2014,127: 148-160.
[7]	Mos N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing[J]. International Journal for Numerical Methods in Engineering,1999,46(1): 131-150.
[8]	Portela A, Aliabadi M H, Rooke D P. Dual boundary element incremental analysis of crack propagation[J]. Computers & Structures,1993,46(2): 237-247.
[9]	Leonel E D, Venturini W S. Dual boundary element formulation applied to analysis of multi-fractured domains[J]. Engineering Analysis With Boundary Elements,2010,34(12): 1092-1099.
[10]	Erdogan. On the stress distribution in a plate with collinear cuts under arbitrary loads[C]// Proceedings of the 〖STBX〗4th US National Congress of Applied Meehanies . 1962: 547-553.
[11]	Tan P W, Raju I S, Newman I, et al. Boundary force method for analyzing two-dimensional cracked bodies[R]. Hampton, Virginia: NASA Langley Research Center, 1986.
[12]	苏成, 郑淳. 基于Erdogan基本解边界元法计算应力强度因子[J]. 力学学报, 2007,39(1): 93-99.(SU Cheng, ZHENG Chun. Calculation of stress intensity factors by boundary element method based on Erdogan fundamental solutions[J]. Chinese Journal of Theoretical and Applied Mechanics,2007,39(1): 93-99.(in Chinese))
[13]	SU Cheng, ZHENG Chun. Probabilistic fracture mechanics analysis of linear-elastic cracked structures by spline fictitious boundary element method[J]. Engineering Analysis With Boundary Elements,2012,36(12): 1828-1837.
[14]	吴家龙. 弹性力学[M]. 上海: 同济大学出版社, 2010.(WU Jia-long. Elasticity Mechanics[M]. Shanghai: Tongji University Press, 2010.(in Chinese))
[15]	Mogilevskaya S G, Linkov A M. Complex fundamental solutions and complex variables boundary element method in elasticity[J]. Computational Mechanics,1998,22(1): 88-92.
[16]	Banerjee P K, Butterifeld R. Boundary Element Method in Engineerng Seienee [M]. London: McGraw Hill, 1981.
[17]	SU Cheng, HAN Da-jian. Multidomain SFBEM and its application in elastic plane problems[J]. Journal of Engineering Mechanics,2000,126(10): 1057-1063.

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含裂纹平面问题Erdogan基本解的显式表达

doi: 10.21656/1000-0887.370253

作者简介:
许秩（1992—），男，博士生(E-mail: stxuz@163.com);范学明（1979—），男，讲师，博士(通讯作者. E-mail: fanxm@scut.edu.cn).

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The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

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含裂纹平面问题Erdogan基本解的显式表达

doi: 10.21656/1000-0887.370253

作者简介: 许秩（1992—），男，博士生(E-mail: stxuz@163.com);范学明 （1979—），男，讲师，博士(通讯作者. E-mail: fanxm@scut.edu.cn).

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出版历程

The Explicit Expression of Erdogan’s Fundamental Solution for Plane Problems With Cracks

计量

出版历程

目录

作者简介:
许秩（1992—），男，博士生(E-mail: stxuz@163.com);范学明（1979—），男，讲师，博士(通讯作者. E-mail: fanxm@scut.edu.cn).